On the old forum you had 24 hrs to edit a post, on the new one this limit was lowered to 120 seconds, Apricot just made a post the other day, which contains this info. The time limit is the same for all member levels. After that time passed by, only mods can edit posts.

If a user edit his/her post, there's always a visible "Last edited: timestamp" note on the post at the bottom right handside. The post you're referring to was made on the old forum and does contain a note like this. The limit to edit a post was 24 hrs on the old forum as i mentioned it above, the OP edited his post inside that limit as you can see it from the timestamp at the bottom.

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